Time or Time Course of Intake

DOE-STD-1121-98

7.4.1 Time or Time Course of Intake

Inference of dose from bioassay data requires a known or assumed time of intake or time course of

intake. In most cases, the time at which an acute intake occurred is either known from observation or

workplace information, can be determined from a variety of factors, or at least can be limited to a small

enough period of time so that bioassay data can be unambiguously interpreted. For chronic or repeated

intakes that occur between bioassay measurements, the pattern in time becomes more problematic.

7.4.1.1 Time Course of Intake to Be Assumed When There Is No Workplace

Evidence

If bioassay results indicate that an intake has occurred, but there is no workplace or other evidence

of an intake, then there are several possibilities:

a non-occupational intake

a deliberate intake

an undetected acute occupational intake

an undetected chronic occupational intake

more than one undetected occupational intake

accidental or deliberate contamination of bioassay samples

error in or sabotage of radiobioassay analytical results

bioassay results have been erroneously associated with the wrong individual.

Each of these possibilities has occurred in the human experience with intakes of radioactive materials.

In the rare case when there is no evidence of when an intake occurred, it is permissible to assume

that the intake occurred at the time when the expectation value of all intakes consistent with a given

bioassay result would have occurred. This assumption is correct on the average and, if always made, will

lead to an unbiased estimate of collective dose in a population. It is also permissible to make the

"midpoint assumption" (See the Time of Intake paragraph in Section 7.3.2.2).

7.4.1.2 A Method for Deducing Time of Intake from Bioassay Data

Assume Q's are retained quantities (in some compartment that can be measured) and a single, acute

intake has occurred. Bioassay measurements show Q1 at one time and Q2 at a time )t later (?). Let t1

denote time between intake and Q1, and Q0 denote amount of initial retained quantity. It is desired to find

the time of intake t1, that is, how long before Q1 intake occurred, and the value of Q0 at the time of intake.

In general, retention functions giving unique relations for a given )t have unique solutions.

However, a single exponential, e!8t, has no unique solution.

Numerical solutions are possible for any retention or excretion functions with other than a single,

linear first-order clearance. Below are analytical solutions for a two-exponential radionuclide retention

function.